... is that it would leave the only ones left with voting rights being the ones least in opposition to the push for war, though the war is itself something that should be accountable to voting rights.

It simply isn't possible to fairly equate being willing to fight a war with having skin in the game. Hell, even if the war is guaranteed to be just and necessary, there are still some problems with the rigor of such an equation: e.g., a) there are different ways to have skin in the game other than being willing to fight, and b) a person might be theoretically willing to fight, but be so opposed to the current war strategy or implementation that they think the war that is just and necessary isn't the one being implemented. Such a person should be able to attempt to do their part to change the nation's course, regardless of whether or not they are legally drafted.